In mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form.
In (Delone & Faddeev 1964), Boris Delone and Dmitriĭ Faddeev showed that binary cubic forms with integer coefficients can be used to parametrize orders in cubic fields. Their work was generalized in (Gan, Gross & Savin 2002, §4) to include all cubic rings, giving a discriminant-preserving bijection between orbits of a GL(2, Z)-action on the space of integral binary cubic forms and cubic rings up to isomorphism.
Read more about Cubic Form: Examples
Famous quotes containing the words cubic and/or form:
“One of the great natural phenomena is the way in which a tube of toothpaste suddenly empties itself when it hears that you are planning a trip, so that when you come to pack it is just a twisted shell of its former self, with not even a cubic millimeter left to be squeezed out.”
—Robert Benchley (1889–1945)
“The novel is the highest form of human expression so far attained. Why? Because it is so incapable of the absolute.”
—D.H. (David Herbert)